No, if the mempool become congested, the fee rate you will use have to be the same or higher than the fee rate the purging is.
It is worth knowing that such transactions are getting confirmed because the mempool is not congested at all to the extent that even 0.3 sat/vbyte transactions are getting confirmed.
I remember spending a lot of money in the past whenever I try to spend and my bad luck is stuck with a congested mempool, even my high fees should wait a couple of blocks before being handled. Luckily it doesn't happen frequently.
Thanks @OP for the explanation, I personally prefer to spend a little above the recommend fees sat/vByte to have a fast confirmation but I wouldn't hesitate to try that if I am not in rush.